Optimal Sensor Placement for Source Localization: A Unified ADMM Approach


Source localization is an important part of many different applications, including radar, wireless Communications, and Communications conducted underwater. There are many different methods for localization, but the ones that rely on Time-of-Arrival (TOA), Time-Difference-Of-Arrival (TDOA), Angle-of-Arrival (AOA), and Received Signal Strength (RSS) are the most common ones. Because the Cramér-Rao lower bounds (CRLB) of these methods explicitly depend on the sensor geometry, the placement of the sensors becomes an extremely important consideration when it comes to applications that involve source localization. Within the scope of this paper, we investigate the possibility of determining the optimum sensor placements for TOA, TDOA, AOA, and RSS-based localization scenarios. To begin, we begin by bringing together the three different localization models through the use of a generalized problem formulation that is centered on the CRLB-related metric. Then, using a combination of the alternating direction method of multipliers (ADMM) and the majorization-minimization (MM) techniques, a unified optimal optimization framework for optimal sensor placement (UTMOST) is developed. The proposed UTMOST, in contrast to the vast majority of works that are considered to be state-of-the-art, neither approximates the design criterion nor takes into account only uncorrelated noise in the measurements. It is easily able to accommodate various design criteria, such as A, D, and E-optimality, with only minor adjustments made within the framework, and it can produce optimal sensor placements in accordance with those criteria. Extensive numerical experiments are carried out in order to demonstrate the usefulness and adaptability of the framework that has been proposed.

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